Mathematical model for determining the position and line tensions for a tethered logging balloon

Abstract:

A program was developed on a desktop computer to determine the cable tensions and position of a balloon tethered by two or more guylines. The program was specifically applied to the analysis of the static load lifting capability of the Pendulum Swing Balloon System. This system uses a tethered balloon and a gravity assisted swing to provide lift and movement to a load of logs.
Due to fundamental differences between conventional cable yarding systems and the pendulum balloon system, a catenary analysis is used to determine cable tensions, balloon position and available lift at a specified load location. Available lift is determined by the tautness of the pendulum, or load carrying line. The length of this line is altered to induce tension into it. The balloon position changes in response to the length adjustment. A gradient search procedure is used in combination with the appropriate catenary equations to conduct the analysis. Comparison of calculated line tensions with selected measurements obtained in a separate field study revealed an average difference of +11.7 percent. Calculated balloon position coordinates were, on the average, within +0.01 percent of the measured positions. A hypothetical setting consisting of a uniform, 60 percent slope extending 2000 feet horizontally was used to evaluate available lift of the system. Guyline placement and corridor orientation were
selected so as to facilitate the analysis. The effect of the pendulum swing was not considered. Results obtained are as fol lows: 1. Total cable weight has a dramatic impact on available lift. If the balloon is to be placed at a high elevation above the ground,
guylines should be made of a material having a higher strength to weight ratio than wire rope. 2. Shortening the pendulum line causes a transfer of tension from adjacent guylines to the pendulum line. The relation of the
load position to the balloon and the original amount of vertical tension in the guylines determines the amount, and rate, of increase
in available lift. In most circumstances, a shortening of 15 feet or less will provide a significant tension transfer without incurring significant balloon movement. Excessive balloon movement will alter the swing capability. 3. If lightweight guylines are used, the balloon should be placed between 1000 and 1500 feet above the 60 percent slope to obtain satisfactory lift at each end of the corridor. The developed model can be used to study the effects of wind, live guylines and cable stretch on the system. Organization of the program is such that harvesting plans for a proposed setting can be developed quickly and easily.